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Mathematics

Assertion (A): 22,23,24,25,26\sqrt{22}, \sqrt{23}, \sqrt{24}, \sqrt{25}, \sqrt{26} and 27\sqrt{27} are irrational numbers between 21\sqrt{21} and 28\sqrt{28}.

Reason (R): 25\sqrt{25} is not an irrational number as 25\sqrt{25} = 5; which is rational number.

  1. A is true, but R is false.

  2. A is false, but R is true.

  3. Both A and R are true, and R is the correct reason for A.

  4. Both A and R are true, and R is the incorrect reason for A.

Rational Irrational Nos

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Answer

Though all the given values 22,23,24,25,26,27\sqrt{22}, \sqrt{23}, \sqrt{24}, \sqrt{25}, \sqrt{26}, \sqrt{27} lie between 21\sqrt{21} and 28\sqrt{28}

But 25\sqrt{25} is not an irrational number, as 25\sqrt{25} = 5, which is a rational number.

∴ A is false, but R is true.

Hence, option 2 is the correct option.

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